Can't believe I didn't see this thread earlier.
OP, if you're still watching, know this: With only one baby, you will no doubt have a
ton of free time on your hands. Plenty of time to sleep, too.
At least, that's how it seems to me and my wife. Ten months ago, she gave birth to triplets.

We still get to play (we're both gamers), pretty much every day. Now that the kids are more or less sleeping through the night, I can get a couple of hours or so at night, and sometimes I can get in some time in the morning too while they're taking a nap.
I never did the whole baby sling thing - well, it wouldn't have worked for us anyway, having 3. So we pretty much only play when they're sleeping, or when the other one of us is watching them.
Actually, I don't even want our kids to
know about computers until they're around 12 or 14. I'm 32. When I was a kid, I played outside and read books. Thank God I didn't have Skyrim and all the digital distractions back then.
Anyway, it's just priorities. And OP, you have to understand that you left yourself wiiiiide open for criticism with the negative-sounding comments earlier in the thread. If I hear that a 30-year-old man finds out he's going to be a dad, and then shares the news with an internet forum 3 hours later while worrying about his inability to play video games, I'm thinking.... Yeah. Western civilization? It's all over, folks.

I do understand where you're coming from, though, and wish you the best.